The discovery of the Higgs boson () by the ATLAS and CMS experiments at the
LHC [1]}, [2]}, [3]}
has opened a new era for particle physics, wherein the characterization of the new boson is of
crucial importance. Studies of the Higgs boson test the standard model (SM) of particle physics and
probe for new physics. Thus far, the properties of the are found
to be consistent with the SM predictions [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}. In particular, nonzero spin assignments
of the have been excluded [11]}, [12]},
and its spin-parity quantum numbers are consistent with
\(J^{PC} = 0^{++}\)  [13]}, [14]}, [11]}, [12]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [12]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}.
However, the limited precision of current
studies allows for anomalous couplings of the with two electroweak gauge bosons (\(\) ) or gluons (\(\) ).
Possible \(CP\) -violating effects in couplings to fermions (\(\) )
have been constrained by the CMS and ATLAS Collaborations in \(\)  production [22]}, [23]}, [33]},
and by the CMS Collaboration in the \(\rightarrow \)  decay [24]},
where \(CP\) -odd couplings may appear at tree level, and are not suppressed by loop effects.
In the SM, \(\)  is mediated via loops, where the top quark dominates. Any observed \(CP\)  violation in the \(\)  interaction would indicate either a \(CP\) -odd Higgs coupling to top quarks (\(\) ) or a new effective interaction requiring
new particles. Thus, a study of the \(\)  coupling provides complementary information on the nature
of the and serves as an indirect search for new phenomena. Both the CMS and ATLAS Collaborations have previously
searched for \(CP\) -violation in the \(\)  coupling, but these constraints are quite weak [23]}, [34]}.
